Bader has been advocating for his topological electron density method (also called AIM for “atoms in molecules”) as the answer to most fundamental chemical issues for a couple of decades now. He summarizes his position regarding molecular structure in a recent paper.1 Here he argues that physics (meaning quantum mechanics) provides a way to uniquely and non-arbitrarily define molecular structure. The atom is defined by the volume enclosed by zero-flux surfaces around a nucleus. The bond path indicates which atoms bind together.

He is careful to indicate that the chemical bond, used in a sort of intuitive way by most chemists, is ill-defined, beyond or outside of physics. His “bond” (or “binding”) is simply the bond path – indicating a pair of interacting atoms.

Bader really wants the union of the bond paths to correspond with the general notion of a bonded molecular structure. He suggests that for all cases, the chemical bonds in a molecule are always observed as bond paths within the electron density. This may be true so far – but certainly we have not examined (computationally nor experimentally) the electron density of all compounds! Equally bothersome is that bond paths occur between atoms for which most chemists would consider to be non-bonded – like between the ortho hydrogens of biphenyl or between hydrogens across the bay region of phenanthrene (see this post). He argues that the barrier for biphenyl rotation arises from the stretching of the C-C bond when the rings become co-planar, but why does this bond stretch in the first place?

While Bader is certainly allowed to call the bond path a “bond”; the question remains whether this definition offers improvements or advantages concerning how we think about and understand molecules, their properties and reactions. To me, this remains an open question.

3 Responses to “AIM analysis and molecular structure”

In section V.3.3 of his article, Bader discusses the role of the Laplacian. It is a short paragraph, and introduces notions of charge concentrations and depletions. Only one example is discussed, that of the structure of chlorine gas as a weakly bound dimer. In appealing to chemists to concentrate on observables, I am surprised at how little Bader choses to focus on this property. Perhaps because, as an observable, it is very difficult to measure (accurately). An example of this is the measured Laplacian for [1.1.1]propellane, in the contentious region of the central C…C “path” (let us avoid the semantically overloaded term bond), which is very different from the calculated value.

However, I venture to suggest in this comment that perhaps as chemists, we should concentrate more on improving our ability to measure the Laplacian. It, after all, does directly probe what the electrons are up to in the region of a bond.

And I offer one final thought. Bader taught us to focus on the so-called critical points in the electron density, introducing the bond-critical point, and with further focus on the value of the Laplacian at that specific point. My own results have shown that the Laplacian may itself be rapidly changing along a bond, and that its value at the BCP may in fact not be at all characteristic of the “bond as a whole” (whatever that means). In other words, the derivative of the Laplacian along the bond may not be zero or small. Perhaps this idea chemists have held ever since Lewis that a chemical bond as a whole has a unique and constant set of properties that fully characterise it is itself in need of a rethink?

I agree on that the usefulness of Bader analysis is still an open question. His claim that quantum mechanics “provides a way to uniquely and non-arbitrarily define molecular structure” is clearly incorrect. A full quantum mechanical description is incompatible with molecular structure.

It is now accepted that one must go beyond the Schrödinger equation (Caldeira-Legget eq., Lindblad eq…) to justify the classical treatment of nuclei. Molecular structure is not the result of a BO approximation, as even now physicists agree, although them now criticize chemists for their belief:

Chemists are used to describing the motion of the nuclei in large molecules classically (for example by rigid configurations), while representing the electrons by wave functions. In general, they attribute this asymmetry to a Born-Oppenheimer approximation. This argument is definitely insufficient, since a straight-forward application of this approximation to molecules would lead to energy (and angular momentum) eigenstates, with vibrational and rotational spectra as known for the hydrogen (or ammonia) molecule.